Abstract
The high velocities observed in supernovae require a relativistic treatment for the equation of motion in the presence of gradients in the density of the interstellar medium. The adopted theory is that of the thin layer approximation. The chosen medium is auto-gravitating with respect to an equatorial plane. The differential equation which governs the relativistic conservation of momentum is solved in numerically and by recursion. The asymmetric field of relativistic velocities as well the time dilation are plotted at the age of 1 yr for SN 1987A.
Highlights
The expansion velocities in supernovae (SN) are quite high and, for example, a time series of eight spectra in SN 2009ig reported that the velocity at the CA II line, decreased from 32,000 km∙s−1 to 21,500 km∙s−1, in 12 days, see Figure 9 in [1]
We briefly recall that the corrections in special relativity (SR) for stable atomic clocks in satellites of the Global Positioning System (GPS) are applied to satellites which are moving at a velocity of ≈3.87 km∙s−1
This first order differential equation can be solved with the Runge-Kutta method, see FORTRAN SUBROUTINE RK4 in [7]
Summary
The expansion velocities in supernovae (SN) are quite high and, for example, a time series of eight spectra in SN 2009ig reported that the velocity at the CA II line, decreased from 32,000 km∙s−1 to 21,500 km∙s−1, in 12 days, see Figure 9 in [1]. We shall discuss a relativistic treatment of the thin layer approximation in the presence of an autogravitating medium
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